Question: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$5.50$, and bags of cookies cost $$3.00$, and sales equaled $$29.00$ in total. There were $4$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5.5x+3y = 29}$ ${y = x+4}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+4}$ for $y$ in the first equation. ${5.5x + 3}{(x+4)}{= 29}$ Simplify and solve for $x$ $ 5.5x+3x + 12 = 29 $ $ 8.5x+12 = 29 $ $ 8.5x = 17 $ $ x = \dfrac{17}{8.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+4}$ to find $y$ ${y = }{(2)}{ + 4}$ ${y = 6}$ You can also plug ${x = 2}$ into $ {5.5x+3y = 29}$ and get the same answer for $y$ ${5.5}{(2)}{ + 3y = 29}$ ${y = 6}$ $2$ bags of candy and $6$ bags of cookies were sold.